Brillouin optical correlation-domain analysis (B-OCDA) allows for distributed measurements of strain and temperature with sub-cm resolution. Time-multiplexing techniques have previously extended B-OCDA to the monitoring of many km of fiber and two million resolution points. Thus far, however, the number of scans of correlation peaks positions, necessary to cover the fiber under test, was restricted to the order of 100 or more. In this work we report a B-OCDA protocol that is able to address an entire fiber using only 11 pairs of position scans per choice of frequency. The measurements protocol relies on a merger between B-OCDA principles and double-pulse-pair analysis, previously incorporated in time-domain Brillouin sensors. Phase coding of the pump and signal waves with a repeating, short and high-rate code stimulates Brillouin interactions in a large number of narrow correlation peaks, with substantial temporal overlap. Unambiguous measurements are achieved by repeating each experiment twice, using a pair of pump pulses of different durations, and subtracting the two output traces. The principle is demonstrated in the analysis of a 43 m-long fiber with 2.7 cm resolution. Several local hot-spots are properly identified in the measurements. The experimental uncertainty in the measurement of the local Brillouin frequency shift is estimated as ± 1.9 MHz. The proposed method requires broader detection bandwidth and a larger number of averages than those of previous time-gated B-OCDA setups. Hence the overall number of measurements is similar to that of previous setups.